A number of Talmudic passages indicate that not every food is equal when it
comes to the vessels in which they may be cooked; some are kallei bishul
(easily cooked items), which get cooked even in a keli sheini (secondary
vessel).

The mishna (145b) says:

Whatever was put into hot water before Shabbat may be steeped in hot water on
Shabbat; but whatever was not put into hot water before Shabbat may be rinsed
with hot water on Shabbat, except for kippers and Spanish mackerel, because
their rinsing concludes their preparation.

We see from this mishna that kippers and Spanish mackerel, foods that are easily
cooked, cant even be rinsed (with hot water) on Shabbat.

Tosafot
(39a, s.v. Kol) cite an argument: is the rinsing mentioned here referring
to
irui
from akelirishon
(primary vessel) or akelisheini?According to the view that this is
the latter, we can clearly see an established law that there are foods that can
be cooked even in a keli sheini.[1]

We can find an additional source in the words of the Gemara (42b) that raises
the possibility that salt can be cooked in a
kelisheini.The
Rishonim do not adopt this ruling,
but we may ask why: it may be that the reason is that nothing could possibly be
cooked in a keli sheini; however it may be that specifically salt does
not cook in a keli sheini, but other items do.

An Additional Problem: The Appearance of Cooking

An additional reason to rule stringently about a keli sheini comes from
the words of
Tosafot
(loc. cit.); in their view,
even though a kelisheini does not cook anything, there
is a rabbinical prohibition to put uncooked items in a
kelisheini, since this is mechzi
ke-mevashel (has the appearance of
bishul).

Even though a keli rishon cooks, this refers specifically to food items
that are easy to cook, such as water, oil, spices and the like; however, foods
that are difficult to cook cannot be cooked in it, just as we conclude
concerning salt to be lenient.
Nevertheless, since we are not experts in the nature of these foods, we forbid
putting anything on Shabbat into a keli sheini, aside from that which is
explicitly allowed in the Gemara.

In his view, there are food items that cannot be cooked even in a keli rishon,
however since we are not experts in the culinary arts and techniques, we are
stringent about a kelirishon for everything.However, the
Ran
indicates that the doubt is about a kelirishon only,
while for a kelisheini there is certainly no
prohibition of bishul at all,
and there is no concern of kalleibishul.[2]

The
Rambam
does not talk about the issue; however, his language (22:6) indicates that he is
lenient:

If one pours a food from a pot to a bowl, even though it is boiling in the bowl,
it is permitted to add spices to the bowl, because a keli sheini does not
cook.

Though the
Rambam
talks about spices, he gives a general justification: a keli sheini does
not cook, and this implies that a keli sheini does not cook at all.It may be that this approach is
based on the understanding that the rule a keli sheini does not cook is
not pragmatic but halakhic 
a kelisheini is not defined as a heat
source that has a prohibition of bishul,
and naturally one is allowed to cook in the keli sheini even those food
items that may end up getting cooked in it.

Yereim: One May Not Put Anything Uncooked in a Secondary Vessel

2.The
Yereim
(ch. 274, 134a) offers a different approach.In his view, since there are foods that are easily cooked, and we cannot
identify them, we may not put anything in a keli that is yad soledet
bo (scalding), despite the fact that he allows putting salt even in a
keli rishon:

Therefore, a person should be careful not to put anything in a keli sheini,
or even in a keli shelishi (tertiary vessel) that is yad soledet bo,
because we are not experts in the definition of soft and hard foods to know
whether they can be cooked in a kelisheini.

The view of the
Yereim
is consistent with the view that the determination that a
kelisheini does not cook is a
pragmatic
assessment, not merely a
halakhic
one, and as long as we do not know with certainty that a food will not cook if
placed in a kelisheini, we must be concerned that it
may belong to the category of kalleibishul.

The Leniency of the Shulchan Arukh

The words of the
Shulchan Arukh
(318:5) indicate that he is lenient about the law of a keli sheini, at
least in reference to bishul achar afiya (cooking after baking):
[3]

There is one who says that if one cooks that which has previously been baked or
fried, this is considered cooking, and thus it would be forbidden to put bread
even in a keli sheini that is yad soledet bo;
however, there are those who allow it.

The
Rema
(ad loc.) explains that the
language of there are those who allow it is meant to be understood as a
leniency specifically for a keli sheini.In other words, essentially there exists a prohibition of cooking after
baking, but there is no prohibition to do so in a keli sheini.This is how the
Mishna Berura
(43) explains: This view holds that a keli sheini cannot cook anything.

It should be noted that there are those who believe that the Shulchan Arukh
is lenient even for a keli rishon, because there is no prohibition on
cooking after an item has been baked (we well get to this in a later shiur)
and according to this, he is not speaking of a keli sheini at all.

The Remas Stringency

However, the
Rema
himself writes that we follow the view of the one who says, and we do not put
bread even into a keli sheini.

It is our preferable custom to be careful not to put bread even into a keli
sheini, as long as it is yad soledet bo.

The
Mishna Berura
(42) explains that according to this view we should be stringent about a keli
sheini, even for other foods, following the
Yereim.
This, according to him, is the law for Ashkenazim:

This view holds that there are items that can be cooked in a keli sheini
because they are soft, and we are not experts.Therefore, he goes further, forbidding putting baked bread, which is
soft, even in a keli sheini.
Similarly, according to this view, we should be stringent about other food items
even in a keli sheini.

The Middle View

3.There are Acharonim who espouse
a middle view:
it is permissible to cook anything in a
kelisheini, excluding foods that
appear to be kalleibishul.This is what the
Shulchan Arukh
(318:25, 44) and the Torat Shabbat (318:16) believe: a
kelisheini does not cook, and one need
not be concerned that everything might fall into the category of
kalleibishul.However, if we observe that a
certain food is easily cookable, one must treat it stringently.As the Arukh Ha-shulchan writes (ad loc.28) about tea leaves:

The plant called tea, over which hot water is poured, is known to be easily
cooked, and even in a keli sheini it will become cooked, as our own eyes
have seen, so one who pours hot water over them on Shabbat, even using a keli
sheini, is liable to bring a sin-offering, and many have stumbled in this

This is also what the
Chazon Ish
writes (52:18-19), that it is possible that the prohibition is specific to baked
goods, as once a food has been baked, it may more easily be cooked.The same would apply to eggs or
other foods that, as we may observe, are easily cooked.When it comes to all other items, it
is permissible to put them in a keli sheini, and one need not be
concerned about this in general.

Practical Law and Custom

In fact, the Ashkenazic custom is to follow the
Mishna Berura,
and Ashkenazim do not put anything that is not cooked in a keli sheini,
due to the concern of kalleibishul.(Even the
Chazon Ish,
who, as mentioned above, supports being lenient about this by the letter of the
law, notes that the custom forbids it).This also appears in Shemirat
Shabbat Ke-hilkhata (1:53).
Among the Sefardic authorities, there are those who write that the custom is to
be lenient (Tevuot Shemesh by Rav Shalom Messas, ch. 30, ch. 66; Tefilla
Le-Moshe vol. I, ch. 33), and there are those who forbid it (Ben Ish Chai,
Year 2, Bo 6; Rav Mordekhai Eliyahu in his notes to Kitzur Shulchan
Arukh, 80:3).Nevertheless, it
makes sense to see the concern about a
kelisheini as a
rabbinical prohibition
only.[4]

Water, Oil and Spices

However, there are certain food items that the Gemara explicitly allows putting
in a kelisheini, ones that are definitely not
kalleibishul: oil (40b), water (42a)[5]
and spices (42b).[6]

What falls into the category of spices?

Onions

The
Taz
(318:8, 14) writes that it is forbidden to put onions in a keli sheini
that is yad soledet bo, since they are sharp and cook quickly.On the other hand, the
Magen Avraham
(15) writes that this is allowed because this is analogous to spices, a view
confirmed by
Shulchan Arukh Ha-Rav
(318:11) and
Arukh Ha-shulchan
(318:44).

On the other hand, the
Mishna Berura
(45) is stringent about this, explaining (Shaar Ha-tziyun 69) that when
the
Magen Avraham
was lenient he was only explaining that according to the views that we are not
concerned about bishul in a
kelisheini, but only about it being
mechzi ke-maveshel, there is no prohibition for onions; however, according
to our view, which is concerned about actual
bishul too, following the path of the
Yereim,
we may not put onions in a kelisheini.
Rav Moshe Feinstein
writes (OC Part 4, 74, Bishul, 18) that an onion is not like spices, and
one should be stringent about it, because it is fit to be eaten on its own, as
opposed to spices; this is evidenced by the law that onions must be tithed even
though spices are exempt from tithing.

Rav Auerbach: Modern Spices are Problematic

Rav Auerbach
is cited (Shemirat Shabbat Ke-hilkhata
ch. 1, n. 152) as claiming that our modern processed spices cannot be equated
with those in the Gemara:

It does not make sense that these are the same spices as those that we use in
order to season our food, as [the latter] are extremely fine; all the more so
will they be cooked in a keli sheini!

Rav Feinstein and Rav Elyashiv: Modern Spices are the Same

However,
Rav Moshe Feinstein
(loc. cit.) writes that cocoa
and coffee are included in the category of spices, and it is permissible to put
them in a keli sheini, even if they have not been cooked and even if they
are finely ground.In his view, it
would appear that even other ground spices may be put in a keli sheini.This is also what is cited in the
name of Rav Elyashiv (Shevut Yitzchak,
Bishul, 24:3), that spices are not
easily cooked, and it does not matter that they have been finely ground:

I have heard from Rav Y.S. Elyashiv that a substance that is hard in its nature,
even though it is ground and made
fine,
does not become easily cookable, since it is not made
soft.[7]

Lemons

The
Chazon Ish
(52:19) allows putting lemons into a keli sheini because it falls into
the category of spices, while
Rav Auerbach
(Shemirat Shabbat Ke-hilkhata, ch. 1,
n. 150) writes that one should not be lenient about this, and
Rav Feinstein
(loc. cit.) writes that one
should be stringent as well.

Cooled Liquids

One should add that the prohibition in a
kelisheini applies to foods that
have never been cooked, but a liquid that has been boiled and cooled may be put
in it (Mishna
Berura
318:23).Indeed, we are stringent
to say that concerning a liquid food (davar lach) there is a prohibition
of cooking, as we shall see in a future shiur, but since this law is the
subject of a dispute of Rishonim, and furthermore most Rishonim believe that a keli
sheini does not cook, these two can together form a good basis for leniency.

Translated by Rav Yoseif Bloch

[1]
This is based on the assumption that the prohibition is one of
bishul, as
Rashi (39a, s.v.
She-hadachato), the Rambam
(9:2) and the Beiur Halakha
(318:4, s.v. Ve-hadachatan) rule. It
is also possible that this is forbidden because of the eclectic melakha
of makkeh ba-pattish, striking the final hammer blow, which includes
various action that complete a process. (This
follows the view of the Peri Megadim,
cited by Beiur Halakhaloc. cit.).

[2]As
for salt, the Ran himself in his
Chiddushim (42b) writes that salt can be cooked in a keli sheini.
The logic is that salt does not
require true bishul;rather,
making it lukewarm is equivalent to cooking it, and therefore it does cook
in a keli sheini. This appears to
be how the Ran explains the law
of Spanish mackerel.In light of
this, something that requires actual
bishul cannot be cooked in a keli sheini, and only concerning kippers
and Spanish mackerel is there any reason to forbid it.

[3]This
is the generally accepted understand of his view, that the halakha follow
the latter view, and this is what Rav Ovadya Yosef writes (Yechaveh Daat,
Vol. II, ch. 44).

[4]In
truth, if we are concerned about kalleibishul, it may be that this is a
biblical doubt. However, since many are
lenient about this, it appears that the ban is only a stringent view, and this
issue should not go beyond the rabbinical level (and naturally one may be
lenient about it in cases of doubt). However,
when it comes to things that may be observed to be
kalleibishul, there is a reason to be
concerned about the doubt of a Torah prohibition.

[5]
According to Shulchan Arukh Ha-Rav
(318:12) and other Acharonim, all liquids have the status of water and
oil, and there is no prohibition to put them in a keli sheini.
However, in the words of the
Mishna Berura (318:39), it
appears that one should be lenient only for water and oil (as he only allows one
to put tea essence and milk in a keli sheini because they have already
been boiled).

[6]
As we mentioned above, the view of
Tosafot is that even when a kelisheini does not cook, there is a
rabbinical prohibition to put uncooked things in a
kelisheini, because it is mechzike-mavashel.
Tosafots words are adopted by the
Mishna Berura (318:34) and other
Acharonim. According to this, why
does the Gemara allow putting certain things in a keli sheini?
Concerning spices,
Tosafot explain themselves that
putting them in does not involve an issue of the appearance of
bishul, since they come only to
impart taste to the food. Concerning water and other liquids, the
Peri Megadim explains (Eshel
Avraham 318:32) that since they are mixed well in the food, this does not
look like cooking. The problem of
mechzi ke-mevashel relates, according to him, only to solid foods soaked in
a liquid contained in a keli sheini, not foods that are mixed in it.

[7]We
may justify this lenient view, by noting that, throughout the Talmud, we find
that spices are referred to as ground, for example in Beitza (14a),
crushed spices  etc. If so, the fact
that the Mishna allows putting spices in a keli sheini without any
limitations apparently indicates that this is allowed for fine spices as well.